116 ANALYTICAL MECHANICS 12. A body, which is dropped from the top of a tower, strikes the ground half a second after it passes by a window 84 feet above the sidewalk. Find the height of the tower. 13. In the preceding problem find the velocity with which the body strikes the ground. 14. A man weighing 150 pounds is obliged to leave his room by way of a window 50 feet above the sidewalk. He has a rope which is long enough, but cannot support more than 125 pounds. What is the least velocity with which he can reach the ground? 16. A ball is dropped in an elevator from a point 6 feet above the floor of the elevator. How long will it take to strike the floor if the elevator is descending with a constant speed of 10 —- ? sec. 106. C. Motion of a Particle along a Smooth Inclined Plane. — There are two forces acting on the particle, its weight and the reaction of the plane. The weight is mg and acts downwards. The reaction of the plane, N; is normal to the plane, because the plane is smooth. Therefore setting the components of the kinetic reaction along and at right angles to the plane equal to FlG' 63" the sum of the corresponding components of the forces we obtain dv m — dt ' Sin a, and a. The last equation states that forces along the normal add up to zero and therefore do not affect the motion. We have, therefore, to consider only the first equation, which gives dv -77 = ff sin a = const.